1 Script Overview

Built with R 3.6.2

This script runs analyses on data from the SPECTRE study. Specifically, it investigates different read-outs as a function of whether participants experienced controllable or uncontrollable stress (or no stress). Measurements under investigation comprised participant ratings (stressor aversiveness, perceived control, stress, helplessness), reaction times, correct responses, and heart rates.

Here we use the following abbreviations: controllable stress = con; uncontrollable stress = noc, baseline = bas.

Linear mixed-effects models were constructed based on the tutorial referenced in Singmann & Kellen, 2019: https://cran.r-project.org/web/packages/afex/vignettes/afex_mixed_example.html

2 Sample Descriptives

N = 45 participants aged 19-30 took part in this study (46.67 % female, age: M = 25, SD = 3.05).

3 Manipulation Checks

3.1 Version Counterbalancing

## 
## 1 2 3 4 5 6 
## 8 8 8 8 6 7

3.2 Yoking of Stress Durations

## 
##  Paired t-test
## 
## data:  stressDur$total_con_stress_dur and stressDur$total_noc_stress_dur
## t = 6.3263, df = 44, p-value = 1.117e-07
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  1.178446 2.280295
## sample estimates:
## mean of the differences 
##                 1.72937
## 
## Cohen's d
## 
## d estimate: 1.004407 (large)
## 95 percent confidence interval:
##    lower    upper 
## 0.559817 1.448996

There was a significant difference in overall stress duration between conditions, yoking did not work out properly. Participants were on average exposed to LESS stress in the uncontrollable condition but reported experiencing no difference or even MORE stress in this condition when asked afterwards. Therefore, effects showing greater performance decrements associated with uncontrollable stress cannot be attributed to more stress. Nevertheless, this remains a limitation.

3.3 Stressor Aversiveness

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: aversiveness ~ condition * run.z + (1 + condition * run.z | id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 2514
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.8211 -0.4516 -0.0157  0.5468  3.1717 
## 
## Random effects:
##  Groups   Name             Variance  Std.Dev. Corr             
##  id       (Intercept)      211.25303 14.5345                   
##           condition1         0.01676  0.1295  -0.29            
##           run.z             49.04422  7.0032   0.42  0.75      
##           condition1:run.z   0.12583  0.3547   0.19  0.88  0.97
##  Residual                   31.04981  5.5722                   
## Number of obs: 356, groups:  id, 45
## 
## Fixed effects:
##                  Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)       63.8384     2.1871  43.8370  29.188  < 2e-16 ***
## condition1        -0.4305     0.2960 252.3147  -1.455  0.14700    
## run.z             -3.7088     1.0866  44.1234  -3.413  0.00139 ** 
## condition1:run.z  -0.2085     0.3004 200.1551  -0.694  0.48850    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtn1 run.z 
## condition1  -0.019              
## run.z        0.399  0.047       
## cndtn1:rn.z  0.034  0.010  0.165
## convergence code: 0
## boundary (singular) fit: see ?isSingular
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: aversiveness ~ condition * run.z + (1 + re1.condition1 + re1.run.z +  
##     re1.condition1_by_run.z || id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 2523
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.9451 -0.4570 -0.0275  0.5309  3.1533 
## 
## Random effects:
##  Groups   Name                    Variance  Std.Dev. 
##  id       (Intercept)             2.101e+02 1.450e+01
##  id.1     re1.condition1          3.370e-14 1.836e-07
##  id.2     re1.run.z               4.907e+01 7.005e+00
##  id.3     re1.condition1_by_run.z 0.000e+00 0.000e+00
##  Residual                         3.125e+01 5.590e+00
## Number of obs: 356, groups:  id, 45
## 
## Fixed effects:
##                  Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)       63.8372     2.1816  43.8455  29.261  < 2e-16 ***
## condition1        -0.4354     0.2963 264.1050  -1.470  0.14286    
## run.z             -3.7103     1.0871  44.1177  -3.413  0.00139 ** 
## condition1:run.z  -0.2151     0.2967 264.1050  -0.725  0.46901    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtn1 run.z
## condition1  0.000              
## run.z       0.001  0.000       
## cndtn1:rn.z 0.000  0.000  0.000
## convergence code: 0
## boundary (singular) fit: see ?isSingular
##  Groups   Name                    Std.Dev.  
##  id       (Intercept)             1.4496e+01
##  id.1     re1.condition1          1.8357e-07
##  id.2     re1.run.z               7.0047e+00
##  id.3     re1.condition1_by_run.z 0.0000e+00
##  Residual                         5.5899e+00
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: aversiveness ~ condition * run.z + (1 + re1.condition1 + re1.run.z ||  
##     id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 2523
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.9451 -0.4570 -0.0275  0.5309  3.1533 
## 
## Random effects:
##  Groups   Name           Variance Std.Dev.
##  id       (Intercept)    210.14   14.496  
##  id.1     re1.condition1   0.00    0.000  
##  id.2     re1.run.z       49.07    7.005  
##  Residual                 31.25    5.590  
## Number of obs: 356, groups:  id, 45
## 
## Fixed effects:
##                  Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)       63.8372     2.1816  43.8455  29.261  < 2e-16 ***
## condition1        -0.4354     0.2963 264.1050  -1.470  0.14286    
## run.z             -3.7103     1.0871  44.1177  -3.413  0.00139 ** 
## condition1:run.z  -0.2151     0.2967 264.1050  -0.725  0.46901    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtn1 run.z
## condition1  0.000              
## run.z       0.001  0.000       
## cndtn1:rn.z 0.000  0.000  0.000
## convergence code: 0
## boundary (singular) fit: see ?isSingular
##  Groups   Name           Std.Dev.
##  id       (Intercept)    14.4963 
##  id.1     re1.condition1  0.0000 
##  id.2     re1.run.z       7.0047 
##  Residual                 5.5899
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: aversiveness ~ condition * run.z + (1 + run.z | id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 2515.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.9268 -0.4541 -0.0162  0.5456  3.1957 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  id       (Intercept) 211.18   14.532       
##           run.z        49.01    7.001   0.42
##  Residual              31.24    5.590       
## Number of obs: 356, groups:  id, 45
## 
## Fixed effects:
##                  Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)       63.8377     2.1869  43.8362  29.191  < 2e-16 ***
## condition1        -0.4354     0.2962 264.1496  -1.470  0.14284    
## run.z             -3.7096     1.0865  44.1244  -3.414  0.00138 ** 
## condition1:run.z  -0.2151     0.2967 264.1496  -0.725  0.46899    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtn1 run.z
## condition1  0.000              
## run.z       0.398  0.000       
## cndtn1:rn.z 0.000  0.000  0.000

## $id

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Data: data
## Models:
## avers.m3c: aversiveness ~ condition * run.z + (1 + run.z | id)
## avers.maxc: aversiveness ~ condition * run.z + (1 + condition * run.z | id)
##            Df    AIC    BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)
## avers.m3c   8 2535.5 2566.5 -1259.8   2519.5                         
## avers.maxc 15 2548.0 2606.2 -1259.0   2518.0 1.5074      7     0.9821
  Fixed Effects - Stressor Aversiveness
Predictors Estimates 95% CI p
Intercept 63.84 59.55 – 68.12 <0.001
Condition -0.44 -1.02 – 0.15 0.143
Run -3.71 -5.84 – -1.58 0.001
Condition x Run -0.22 -0.80 – 0.37 0.469
Random Effects
σ2 31.24
τ00 id 211.18
τ11 id.run.z 49.01
ρ01 id 0.42
ICC 0.89
N id 45
Marginal R2 / Conditional R2 0.046 / 0.898

Participants rated the stressor as very aversive in both controllable and uncontrollable trials (global M = 63.75). In both conditions, aversiveness ratings decreased slightly over runs.

3.4 Perceived Control

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: control ~ condition * run.z + (1 + condition * run.z | id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 3039.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.3519 -0.4355  0.0359  0.4547  3.0173 
## 
## Random effects:
##  Groups   Name             Variance Std.Dev. Corr             
##  id       (Intercept)      130.72   11.433                    
##           condition1        95.47    9.771   -0.06            
##           run.z             35.15    5.929    0.25 -0.03      
##           condition1:run.z  14.02    3.745   -0.16  0.60 -0.29
##  Residual                  164.98   12.845                    
## Number of obs: 356, groups:  id, 45
## 
## Fixed effects:
##                  Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)       48.2227     1.8367 44.2129  26.255  < 2e-16 ***
## condition1        16.4509     1.6089 44.2375  10.225 3.15e-13 ***
## run.z              0.8853     1.1206 39.7904   0.790   0.4342    
## condition1:run.z   1.8034     0.8850 44.3395   2.038   0.0476 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtn1 run.z 
## condition1  -0.050              
## run.z        0.190 -0.022       
## cndtn1:rn.z -0.093  0.344 -0.146

## $id
  Fixed Effects - Perceived Control
Predictors Estimates 95% CI p
Intercept 48.22 44.62 – 51.82 <0.001
Condition 16.45 13.30 – 19.60 <0.001
Run 0.89 -1.31 – 3.08 0.434
Condition x Run 1.80 0.07 – 3.54 0.048
Random Effects
σ2 164.98
τ00 id 130.72
τ11 id.condition1 95.47
τ11 id.run.z 35.15
τ11 id.condition1:run.z 14.02
ρ01 -0.06
0.25
-0.16
ICC 0.63
N id 45
Marginal R2 / Conditional R2 0.385 / 0.769

Participants reported higher perceived control under controllable trials compared to uncontrollable trials. Ratings increased over runs for controllable stress, but decreased for uncontrollable stress.

4 Ratings

4.1 Stress

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: stress ~ condition + (1 + condition * run.z | id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 4264
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.9127 -0.3974 -0.0433  0.3793  4.2869 
## 
## Random effects:
##  Groups   Name             Variance Std.Dev. Corr                         
##  id       (Intercept)      269.274  16.410                                
##           condition1       179.736  13.407   -0.23                        
##           condition2        65.835   8.114    0.20 -0.78                  
##           run.z             24.931   4.993    0.16  0.13  0.02            
##           condition1:run.z   7.861   2.804   -0.51  0.05 -0.12 -0.93      
##           condition2:run.z   2.471   1.572    0.22 -0.02  0.58  0.55 -0.53
##  Residual                   81.216   9.012                                
## Number of obs: 534, groups:  id, 45
## 
## Fixed effects:
##             Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)   38.663      2.356  44.138  16.411  < 2e-16 ***
## condition1   -17.691      2.051  44.049  -8.626 5.14e-11 ***
## condition2     7.437      1.299  44.626   5.723 8.24e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1 -0.223       
## condition2  0.186 -0.765
## convergence code: 0
## boundary (singular) fit: see ?isSingular
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## stress ~ condition + (1 + re1.condition1 + re1.condition2 + re1.run.z +  
##     re1.condition1_by_run.z + re1.condition2_by_run.z || id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 4323.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.4502 -0.3849 -0.0329  0.3338  4.0466 
## 
## Random effects:
##  Groups   Name                    Variance Std.Dev.
##  id       (Intercept)             266.691  16.331  
##  id.1     re1.condition1          162.838  12.761  
##  id.2     re1.condition2           58.278   7.634  
##  id.3     re1.run.z                24.409   4.941  
##  id.4     re1.condition1_by_run.z   5.207   2.282  
##  id.5     re1.condition2_by_run.z   0.000   0.000  
##  Residual                          85.267   9.234  
## Number of obs: 534, groups:  id, 45
## 
## Fixed effects:
##             Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)   36.930      2.468  44.014  14.967  < 2e-16 ***
## condition1   -18.246      1.985  43.951  -9.193 8.48e-12 ***
## condition2     7.110      1.271  44.057   5.595 1.32e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1  0.000       
## condition2  0.000 -0.063
## convergence code: 0
## boundary (singular) fit: see ?isSingular
##  Groups   Name                    Std.Dev.
##  id       (Intercept)             16.3307 
##  id.1     re1.condition1          12.7608 
##  id.2     re1.condition2           7.6340 
##  id.3     re1.run.z                4.9406 
##  id.4     re1.condition1_by_run.z  2.2820 
##  id.5     re1.condition2_by_run.z  0.0000 
##  Residual                          9.2340
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: stress ~ condition + (1 + condition + run.z | id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 4290.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.5270 -0.3883 -0.0462  0.3709  4.1945 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr             
##  id       (Intercept) 267.24   16.347                    
##           condition1  180.09   13.420   -0.24            
##           condition2   64.51    8.032    0.20 -0.79      
##           run.z        23.98    4.897    0.14  0.15 -0.01
##  Residual              89.41    9.456                    
## Number of obs: 534, groups:  id, 45
## 
## Fixed effects:
##             Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)   37.888      2.453  43.999  15.443  < 2e-16 ***
## condition1   -17.387      2.067  44.034  -8.412 1.04e-10 ***
## condition2     7.098      1.330  44.102   5.336 3.13e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1 -0.244       
## condition2  0.178 -0.748

## $id

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Data: data
## Models:
## stress.m2c: stress ~ condition + (1 + condition + run.z | id)
## stress.maxc: stress ~ condition + (1 + condition * run.z | id)
##             Df    AIC    BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)   
## stress.m2c  14 4327.4 4387.3 -2149.7   4299.4                            
## stress.maxc 25 4322.3 4429.3 -2136.1   4272.3 27.104     11   0.004433 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##  condition emmean   SE df lower.CL upper.CL
##  bas         20.5 2.86 44     14.7     26.3
##  con         45.0 3.06 44     38.8     51.2
##  noc         48.2 3.11 44     41.9     54.4
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95
##  contrast  estimate   SE df t.ratio p.value
##  bas - con   -24.48 3.26 44 -7.515  <.0001 
##  bas - noc   -27.68 3.33 44 -8.300  <.0001 
##  con - noc    -3.19 1.81 44 -1.765  0.0845 
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: holm method for 3 tests
  Fixed Effects - Stress
Predictors Estimates 95% CI p
Intercept 37.89 33.08 – 42.70 <0.001
Condition-CON -17.39 -21.44 – -13.34 <0.001
Condition-UNCON 7.10 4.49 – 9.70 <0.001
Random Effects
σ2 89.41
τ00 id 267.24
τ11 id.condition1 180.09
τ11 id.condition2 64.51
τ11 id.run.z 23.98
ρ01 -0.24
0.20
0.14
ICC 0.81
N id 45
Marginal R2 / Conditional R2 0.249 / 0.855
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## stress ~ condition * aversiveness.z + (1 + condition * aversiveness.z +  
##     run | id) + (1 | run)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 2869.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.9148 -0.3764 -0.0081  0.3585  3.8930 
## 
## Random effects:
##  Groups   Name                      Variance  Std.Dev.  Corr                   
##  id       (Intercept)               4.539e+02 2.131e+01                        
##           condition1                1.365e+01 3.695e+00 -0.24                  
##           aversiveness.z            4.617e+01 6.795e+00 -0.45 -0.64            
##           run                       1.624e+01 4.030e+00 -0.61  0.31  0.44      
##           condition1:aversiveness.z 8.834e+00 2.972e+00  0.52  0.70 -0.95 -0.28
##  run      (Intercept)               5.836e-14 2.416e-07                        
##  Residual                           1.014e+02 1.007e+01                        
## Number of obs: 356, groups:  id, 45; run, 4
## 
## Fixed effects:
##                           Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)                46.7521     2.6390 41.1145  17.716  < 2e-16 ***
## condition1                 -2.3315     0.7898 42.4630  -2.952  0.00513 ** 
## aversiveness.z              4.9076     1.5789 23.0594   3.108  0.00494 ** 
## condition1:aversiveness.z   1.0953     0.7849 36.2080   1.395  0.17138    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtn1 avrsv.
## condition1  -0.112              
## aversvnss.z -0.179 -0.255       
## cndtn1:vrs.  0.222  0.335 -0.467
## convergence code: 0
## boundary (singular) fit: see ?isSingular

Participants reported higher stress levels in both stress conditions compared to baseline. There was no difference in stress ratings between controllable and uncontrollable stress trials.

4.2 Helplessness

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: helplessness ~ condition + (1 + condition * run.z | id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 3101.4
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.94525 -0.41873 -0.04023  0.40994  2.80271 
## 
## Random effects:
##  Groups   Name             Variance Std.Dev. Corr             
##  id       (Intercept)      309.894  17.604                    
##           condition1       138.468  11.767   -0.13            
##           run.z             36.530   6.044    0.13 -0.12      
##           condition1:run.z   8.092   2.845   -0.28  0.47  0.03
##  Residual                  173.027  13.154                    
## Number of obs: 356, groups:  id, 45
## 
## Fixed effects:
##             Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)   46.389      2.676  44.049  17.337  < 2e-16 ***
## condition1   -10.338      1.831  44.006  -5.647 1.11e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr)
## condition1 -0.076

## $id
  Fixed Effects - Helplessness
Predictors Estimates 95% CI p
Intercept 46.39 41.14 – 51.63 <0.001
Condition -10.34 -13.93 – -6.75 <0.001
Random Effects
σ2 173.03
τ00 id 309.89
τ11 id.condition1 138.47
τ11 id.run.z 36.53
τ11 id.condition1:run.z 8.09
ρ01 -0.13
0.13
-0.28
ICC 0.72
N id 45
Marginal R2 / Conditional R2 0.147 / 0.763

Participants reported feeling less helpless in controllable trials compared to uncontrollable trials.

5 Reaction Times (RT)

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: rt ~ condition + (1 + condition * run.z | id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 58677
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.0075 -0.6585 -0.0145  0.6385  3.3779 
## 
## Random effects:
##  Groups   Name             Variance Std.Dev. Corr                         
##  id       (Intercept)       2271.04  47.655                               
##           condition1         302.99  17.406  -0.29                        
##           condition2          70.71   8.409   0.27 -0.98                  
##           run.z               69.52   8.338   0.24  0.18 -0.25            
##           condition1:run.z   124.89  11.175   0.19 -0.26  0.32 -0.40      
##           condition2:run.z    39.75   6.305   0.06  0.00 -0.16  0.82 -0.39
##  Residual                  10580.93 102.864                               
## Number of obs: 4830, groups:  id, 45
## 
## Fixed effects:
##             Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)  772.749      7.157  43.610 107.974  < 2e-16 ***
## condition1    18.834      3.591  42.188   5.244 4.75e-06 ***
## condition2   -27.254      2.405  61.588 -11.334  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1 -0.146       
## condition2  0.101 -0.723
## convergence code: 0
## boundary (singular) fit: see ?isSingular
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: rt ~ condition + (1 + re1.condition1 + re1.condition2 + re1.run +  
##     re1.condition1_by_run + re1.condition2_by_run || id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 58700.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.9114 -0.6512 -0.0144  0.6349  3.2258 
## 
## Random effects:
##  Groups   Name                  Variance  Std.Dev.
##  id       (Intercept)            2153.106  46.402 
##  id.1     re1.condition1          110.125  10.494 
##  id.2     re1.condition2            0.000   0.000 
##  id.3     re1.run                  55.606   7.457 
##  id.4     re1.condition1_by_run     1.105   1.051 
##  id.5     re1.condition2_by_run     0.000   0.000 
##  Residual                       10716.215 103.519 
## Number of obs: 4830, groups:  id, 45
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)  773.808      7.414   43.343 104.368  < 2e-16 ***
## condition1    18.759      3.020   74.976   6.212 2.67e-08 ***
## condition2   -27.113      2.085 4699.506 -13.006  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1  0.063       
## condition2 -0.046 -0.514
## convergence code: 0
## boundary (singular) fit: see ?isSingular
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: rt ~ condition + (1 + re1.condition1 + re1.condition2 + re1.run ||  
##     id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 58700.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.9107 -0.6510 -0.0143  0.6347  3.2269 
## 
## Random effects:
##  Groups   Name           Variance Std.Dev.
##  id       (Intercept)     2151.97  46.389 
##  id.1     re1.condition1   115.35  10.740 
##  id.2     re1.condition2     0.00   0.000 
##  id.3     re1.run           55.61   7.457 
##  Residual                10717.58 103.526 
## Number of obs: 4830, groups:  id, 45
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)  773.805      7.413   43.357 104.392  < 2e-16 ***
## condition1    18.750      3.014   78.577   6.221 2.24e-08 ***
## condition2   -27.110      2.085 4709.384 -13.003  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1  0.063       
## condition2 -0.046 -0.515
## convergence code: 0
## boundary (singular) fit: see ?isSingular
##  Groups   Name           Std.Dev.
##  id       (Intercept)     46.3894
##  id.1     re1.condition1  10.7399
##  id.2     re1.condition2   0.0000
##  id.3     re1.run          7.4573
##  Residual                103.5257
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: rt ~ condition + (1 + run | id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 58705.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.9583 -0.6519 -0.0177  0.6412  3.1763 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr 
##  id       (Intercept)  2491.75  49.917       
##           run            68.54   8.279  -0.26
##  Residual             10768.09 103.769       
## Number of obs: 4830, groups:  id, 45
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)  772.625      7.415   44.147 104.195  < 2e-16 ***
## condition1    18.677      2.553 4744.938   7.317 2.96e-13 ***
## condition2   -27.056      2.089 4741.674 -12.951  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1  0.075       
## condition2 -0.046 -0.609

## $id

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Data: data
## Models:
## rt.m3c: rt ~ condition + (1 + run | id)
## rt.maxc: rt ~ condition + (1 + condition * run.z | id)
##         Df   AIC   BIC logLik deviance  Chisq Chi Df Pr(>Chisq)  
## rt.m3c   7 58732 58777 -29359    58718                           
## rt.maxc 25 58740 58902 -29345    58690 28.014     18    0.06184 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##  condition emmean   SE  df asymp.LCL asymp.UCL
##  bas          791 8.02 Inf       776       807
##  con          746 7.61 Inf       731       760
##  noc          781 7.61 Inf       766       796
## 
## Degrees-of-freedom method: asymptotic 
## Confidence level used: 0.95
##  contrast  estimate   SE  df z.ratio p.value
##  bas - con     45.7 4.17 Inf  10.972 <.0001 
##  bas - noc     10.3 4.18 Inf   2.466 0.0137 
##  con - noc    -35.4 3.31 Inf -10.690 <.0001 
## 
## Degrees-of-freedom method: asymptotic 
## P value adjustment: holm method for 3 tests
  Fixed Effects - Reaction Times
Predictors Estimates 95% CI p
Intercept 772.62 758.09 – 787.16 <0.001
Condition-CON 18.68 13.67 – 23.68 <0.001
Condition-UNCON -27.06 -31.15 – -22.96 <0.001
Random Effects
σ2 10768.09
τ00 id 2491.75
τ11 id.run 68.54
ρ01 id -0.26
ICC 0.19
N id 45
Marginal R2 / Conditional R2 0.028 / 0.210

Reaction times were shorter under stress compared to baseline. Further, participants responded faster in the controllable condition compared to the uncontrollable condition.

6 Correct Responses

## Fitting 2 (g)lmer() models:
## [..]
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: correct ~ condition + (1 + condition * run.z | id)
##    Data: data
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
##      AIC      BIC   logLik deviance df.resid 
##   3654.0   3810.8  -1803.0   3606.0     5075 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -5.1084  0.2270  0.2946  0.3992  0.9212 
## 
## Random effects:
##  Groups Name             Variance Std.Dev. Corr                         
##  id     (Intercept)      0.493487 0.70249                               
##         condition1       0.009456 0.09724  -0.36                        
##         condition2       0.005575 0.07466  -0.82  0.59                  
##         run.z            0.050323 0.22433  -0.18 -0.85 -0.17            
##         condition1:run.z 0.051431 0.22678   0.75  0.31 -0.54 -0.73      
##         condition2:run.z 0.061799 0.24859  -0.69  0.01  0.17  0.38 -0.49
## Number of obs: 5099, groups:  id, 44
## 
## Fixed effects:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  2.20180    0.13325  16.523  < 2e-16 ***
## condition1  -0.34078    0.09302  -3.664 0.000249 ***
## condition2   0.30334    0.08588   3.532 0.000412 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1 -0.028       
## condition2 -0.163 -0.538
## convergence code: 0
## boundary (singular) fit: see ?isSingular
## Fitting 2 (g)lmer() models:
## [..]
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: correct ~ condition + (1 + re1.condition1 + re1.condition2 +  
##     re1.run.z + re1.condition1_by_run.z + re1.condition2_by_run.z ||      id)
##    Data: data
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
##      AIC      BIC   logLik deviance df.resid 
##   3638.3   3697.1  -1810.1   3620.3     5090 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -5.0614  0.2322  0.3016  0.3987  0.8710 
## 
## Random effects:
##  Groups Name                    Variance Std.Dev.
##  id     (Intercept)             0.49878  0.7062  
##  id.1   re1.condition1          0.00000  0.0000  
##  id.2   re1.condition2          0.00000  0.0000  
##  id.3   re1.run.z               0.05822  0.2413  
##  id.4   re1.condition1_by_run.z 0.01614  0.1271  
##  id.5   re1.condition2_by_run.z 0.04772  0.2184  
## Number of obs: 5099, groups:  id, 44
## 
## Fixed effects:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  2.08802    0.11806  17.686  < 2e-16 ***
## condition1  -0.32386    0.06730  -4.812 1.49e-06 ***
## condition2   0.30626    0.06293   4.867 1.13e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1  0.053       
## condition2 -0.006 -0.577
## convergence code: 0
## boundary (singular) fit: see ?isSingular
##  Groups Name                    Std.Dev.
##  id     (Intercept)             0.70625 
##  id.1   re1.condition1          0.00000 
##  id.2   re1.condition2          0.00000 
##  id.3   re1.run.z               0.24128 
##  id.4   re1.condition1_by_run.z 0.12706 
##  id.5   re1.condition2_by_run.z 0.21844
## Fitting 2 (g)lmer() models:
## [..]
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: correct ~ condition + (1 + run.z | id)
##    Data: data
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
##      AIC      BIC   logLik deviance df.resid 
##   3636.6   3675.9  -1812.3   3624.6     5093 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -5.1134  0.2358  0.3061  0.3976  0.9264 
## 
## Random effects:
##  Groups Name        Variance Std.Dev. Corr 
##  id     (Intercept) 0.49329  0.7023        
##         run.z       0.05608  0.2368   -0.09
## Number of obs: 5099, groups:  id, 44
## 
## Fixed effects:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  2.09322    0.13820  15.146  < 2e-16 ***
## condition1  -0.31162    0.06688  -4.659 3.17e-06 ***
## condition2   0.30358    0.06200   4.897 9.74e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1  0.052       
## condition2 -0.006 -0.582

## $id

## Fitting 2 (g)lmer() models:
## [..]
## Fitting 2 (g)lmer() models:
## [..]
## Data: data
## Models:
## corr.m2c: correct ~ condition + (1 + run.z | id)
## corr.maxc: correct ~ condition + (1 + condition * run.z | id)
##           Df    AIC    BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)
## corr.m2c   6 3636.6 3675.9 -1812.3   3624.6                         
## corr.maxc 24 3654.0 3810.8 -1803.0   3606.0 18.672     18     0.4123
##  condition emmean    SE  df asymp.LCL asymp.UCL
##  bas         1.78 0.157 Inf      1.47      2.09
##  con         2.40 0.151 Inf      2.10      2.69
##  noc         2.10 0.147 Inf      1.81      2.39
## 
## Results are given on the logit (not the response) scale. 
## Confidence level used: 0.95
##  contrast  estimate    SE  df z.ratio p.value
##  bas - con   -0.615 0.115 Inf -5.367  <.0001 
##  bas - noc   -0.320 0.110 Inf -2.908  0.0069 
##  con - noc    0.296 0.101 Inf  2.927  0.0069 
## 
## Results are given on the log odds ratio (not the response) scale. 
## P value adjustment: holm method for 3 tests
  Fixed Effects - Correct Responses
Predictors Estimates 95% CI p
Intercept 2.09 1.82 – 2.36 <0.001
Condition-CON -0.31 -0.44 – -0.18 <0.001
Condition-UNCON 0.30 0.18 – 0.43 <0.001
Random Effects
σ2 3.29
τ00 id 0.49
τ11 id.run.z 0.06
ρ01 id -0.09
ICC 0.13
N id 44
Marginal R2 / Conditional R2 0.014 / 0.142

Performance was significantly better (higher rate of correct responses) under stress compared to baseline. Further, participants responded correctly more often in the controllable condition compared to the uncontrollable condition.

7 Heart Rate (HR)

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: bpm ~ condition + (1 + condition * run | id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 2475
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.8671 -0.4801 -0.0130  0.4876  6.6171 
## 
## Random effects:
##  Groups   Name           Variance Std.Dev. Corr                         
##  id       (Intercept)    214.6552 14.6511                               
##           condition1       1.3146  1.1465  -0.87                        
##           condition2       3.5769  1.8913   0.75 -0.98                  
##           run              6.9078  2.6283  -0.68  0.95 -0.99            
##           condition1:run   0.1157  0.3402   0.98 -0.95  0.86 -0.80      
##           condition2:run   0.3544  0.5953  -0.78  0.98 -1.00  0.99 -0.88
##  Residual                  5.9750  2.4444                               
## Number of obs: 462, groups:  id, 42
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)  62.4823     1.6336  41.3321  38.247   <2e-16 ***
## condition1   -0.2225     0.1631 288.0715  -1.364    0.174    
## condition2    0.2088     0.1619 364.2497   1.290    0.198    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1  0.122       
## condition2 -0.009 -0.503
## convergence code: 0
## boundary (singular) fit: see ?isSingular
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: bpm ~ condition + (1 + re1.condition1 + re1.condition2 + re1.run.z +  
##     re1.condition1_by_run.z + re1.condition2_by_run.z || id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 2497.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.4961 -0.4922 -0.0164  0.4284  6.5400 
## 
## Random effects:
##  Groups   Name                    Variance  Std.Dev. 
##  id       (Intercept)             1.217e+02 1.103e+01
##  id.1     re1.condition1          0.000e+00 0.000e+00
##  id.2     re1.condition2          2.024e-14 1.423e-07
##  id.3     re1.run.z               8.182e+00 2.860e+00
##  id.4     re1.condition1_by_run.z 0.000e+00 0.000e+00
##  id.5     re1.condition2_by_run.z 0.000e+00 0.000e+00
##  Residual                         6.353e+00 2.521e+00
## Number of obs: 462, groups:  id, 42
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)  65.0530     1.7067  41.0029  38.117  < 2e-16 ***
## condition1   -0.5347     0.1658 375.7917  -3.224  0.00138 ** 
## condition2    0.5405     0.1658 375.7917   3.259  0.00122 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1  0.000       
## condition2  0.000 -0.500
## convergence code: 0
## boundary (singular) fit: see ?isSingular
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: bpm ~ condition + (1 + re1.condition1 + re1.condition2 + re1.run ||  
##     id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 2506.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.5784 -0.4898 -0.0148  0.4131  6.5227 
## 
## Random effects:
##  Groups   Name           Variance  Std.Dev. 
##  id       (Intercept)    1.496e+02 1.223e+01
##  id.1     re1.condition1 0.000e+00 0.000e+00
##  id.2     re1.condition2 1.346e-16 1.160e-08
##  id.3     re1.run        6.614e+00 2.572e+00
##  Residual                6.370e+00 2.524e+00
## Number of obs: 462, groups:  id, 42
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)  69.9501     1.9112  40.9847  36.600  < 2e-16 ***
## condition1   -0.5347     0.1661 373.8711  -3.220  0.00140 ** 
## condition2    0.5405     0.1661 373.8711   3.255  0.00124 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1  0.000       
## condition2  0.000 -0.500
## convergence code: 0
## boundary (singular) fit: see ?isSingular
##  Groups   Name           Std.Dev.  
##  id       (Intercept)    1.2231e+01
##  id.1     re1.condition1 0.0000e+00
##  id.2     re1.condition2 1.1602e-08
##  id.3     re1.run        2.5717e+00
##  Residual                2.5239e+00
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: bpm ~ condition + (1 + run | id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 2495.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.4130 -0.4908 -0.0258  0.4270  6.5567 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr 
##  id       (Intercept) 218.602  14.785        
##           run           6.776   2.603   -0.69
##  Residual               6.353   2.521        
## Number of obs: 462, groups:  id, 42
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)  62.1988     1.6732  41.1307  37.174  < 2e-16 ***
## condition1   -0.5347     0.1658 375.8260  -3.224  0.00137 ** 
## condition2    0.5405     0.1658 375.8260   3.259  0.00122 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) cndtn1
## condition1  0.000       
## condition2  0.000 -0.500

## $id

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Data: data
## Models:
## hr.m3c: bpm ~ condition + (1 + run | id)
## hr.maxc: bpm ~ condition + (1 + condition * run | id)
##         Df    AIC    BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)
## hr.m3c   7 2508.8 2537.8 -1247.4   2494.8                         
## hr.maxc 25 2523.8 2627.2 -1236.9   2473.8 20.986     18     0.2801
##  condition emmean   SE   df lower.CL upper.CL
##  bas         61.7 1.72 41.8     58.2     65.1
##  con         62.7 1.72 41.8     59.3     66.2
##  noc         62.2 1.72 41.8     58.7     65.7
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95
##  contrast  estimate    SE  df t.ratio p.value
##  bas - con   -1.075 0.287 376 -3.743  0.0006 
##  bas - noc   -0.529 0.287 376 -1.841  0.1159 
##  con - noc    0.546 0.287 376  1.902  0.1159 
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: holm method for 3 tests
  Fixed Effects - Heart Rate
Predictors Estimates 95% CI p
Intercept 62.20 58.92 – 65.48 <0.001
Condition-CON -0.53 -0.86 – -0.21 0.001
Condition-UNCON 0.54 0.22 – 0.87 0.001
Random Effects
σ2 6.35
τ00 id 218.60
τ11 id.run 6.78
ρ01 id -0.69
ICC 0.97
N id 42
Marginal R2 / Conditional R2 0.001 / 0.972

Heart rates were higher under controllable stress compared to baseline. No other contrasts were significant.

8 MR Parameter Estimates

8.1 Does vmPFC activation modulate ratings?

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: stress ~ condition * beta_weight.z + (1 + condition + run.z |      id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 2734
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.2382 -0.3921 -0.0011  0.3647  3.9295 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr     
##  id       (Intercept) 349.28   18.689            
##           condition1   25.34    5.034   0.01     
##           run.z        34.63    5.884   0.36 0.18
##  Residual             102.65   10.132            
## Number of obs: 336, groups:  id, 42
## 
## Fixed effects:
##                          Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)               49.6090     2.8049  41.2989  17.686   <2e-16 ***
## condition1                -1.3897     0.9560  42.0390  -1.454    0.153    
## beta_weight.z             -0.4732     0.8183 278.5410  -0.578    0.564    
## condition1:beta_weight.z   0.2263     0.6945 263.5330   0.326    0.745    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtn1 bt_wg.
## condition1  -0.037              
## beta_wght.z  0.039 -0.145       
## cndtn1:bt_. -0.047 -0.007  0.041
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: helplessness ~ condition * beta_weight.z + (1 + condition * run.z |  
##     id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
## 
## REML criterion at convergence: 2916.3
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.92315 -0.43201 -0.04629  0.39820  2.85392 
## 
## Random effects:
##  Groups   Name             Variance Std.Dev. Corr             
##  id       (Intercept)      305.192  17.470                    
##           condition1       134.433  11.595   -0.06            
##           run.z             33.159   5.758    0.23 -0.26      
##           condition1:run.z   7.446   2.729   -0.16  0.37  0.15
##  Residual                  174.531  13.211                    
## Number of obs: 336, groups:  id, 42
## 
## Fixed effects:
##                           Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)               47.48103    2.74810  41.50394  17.278  < 2e-16 ***
## condition1               -10.96352    1.87977  42.26682  -5.832 6.78e-07 ***
## beta_weight.z              0.02837    1.05541 275.34053   0.027   0.9786    
## condition1:beta_weight.z   2.04439    0.98787 244.65767   2.069   0.0395 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtn1 bt_wg.
## condition1  -0.009              
## beta_wght.z  0.024 -0.137       
## cndtn1:bt_. -0.085  0.031  0.065
  Fixed Effects - Helplessness
Predictors Estimates 95% CI p
Intercept 47.48 42.09 – 52.87 <0.001
Condition -10.96 -14.65 – -7.28 <0.001
Beta Weight 0.03 -2.04 – 2.10 0.979
Condition x Beta Weight 2.04 0.11 – 3.98 0.040
Random Effects
σ2 174.53
τ00 id 305.19
τ11 id.condition1 134.43
τ11 id.run.z 33.16
τ11 id.condition1:run.z 7.45
ρ01 -0.06
0.23
-0.16
ICC 0.72
N id 42
Marginal R2 / Conditional R2 0.169 / 0.764

VmPFC activation modulated helplessness ratings for uncontrollable stress, not for controllable stress. For uncontrollable stress, higher beta weights were linked to lower helplessness ratings.

9 Correction for Multiple Dependent Variables

##             DV p.orig Bonferroni
## 2 helplessness 0.0001     0.0005
## 3           RT 0.0001     0.0005
## 4      correct 0.0069     0.0345
## 1       stress 0.0845     0.4225
## 5           hr 0.1159     0.5795

10 Figures for Paper